年間 4 号発行
ISSN 印刷: 1099-2391
ISSN オンライン: 2641-7359
ANALYTICAL SOLUTION OF THE EXTENDED GRAETZ PROBLEM WITH AXIAL CONDUCTION AND CONVECTIVE BOUNDARY CONDITIONS
要約
This article presents an analytical solution to the extended Graetz problem, in a circular pipe, with axial heat conduction, subjected to boundary conditions of the third kind. A mathematical scheme for solving this type of heat transfer problem was proposed by the present authors [1]. The solution employs a complete basis for the set of square integrable functions, orthogonal to the Hermite polynomials. The temperature profile is obtained as an infinite series of products of functions, resulting in decomposition of the energy equation into a set of ordinary differential equations, each of which depends on the two previous equations only. This allows a straightforward solution of the set of equations. The effects of the external Biot number and the axial conduction in fluid on the surface temperature, bulk temperature, heat flux, and Nusselt number are shown.